1. Is this a luggage door or the main cabin door? Wondering if there's a different alert.
This is the main passenger door. The cargo door (and every other door on the airplane) is a plug-type door, and therefore cannot open while the aircraft is in the air. The passenger door is not a plug, it is just held in place by many pins and cam-locks. On the CRJ, the passenger door being open generates a red warning message, while every other door generates a yellow caution message.
2. Why didn't he declare an emergency? I realize it's his option, but with 15 on board, why not?
Not sure. Pilot's discretion. Although the door indicated open, it obviously wasn't actually open (or else this would be a completely different thread, and the ferry boats would have had another outing). The crew knew this and just did a standard return to departure airport. Most mechanical returns are not emergencies. Many diversions are (since it is something to land right away for, rather than continuing).
3. Finally, the discussion on the return set up is great... Can or shouldn't the flight computer be set up for an emergency return and also the destination? Press a button and get that return? Or can only the final destination be set up?
The FMS has certain logic to its menu systems. SIDs for the departure airport, STARs and approaches for the destination. They certainly could have changed the destination airport in the FMS to KJFK and had the approaches available. This would require just a couple steps of changing the destination, making KJFK the next waypoint (which would clear the original flight plan route), then selecting the approach the wanted. But why go through all of that when you can just look out your left window and see the airport 5 miles away. Automation is made to assist the pilot, but sometimes using less automation is easier.